Polynomial B-splines of given order m and with knots of arbitrary multiplicity are investigated with respect to their Chebyshev norm. We present a complete characterization of those B~splines with maximal and with minimal norm, compute these norms explicitly and study their behavior as m tends to infinity. Furthermore, the norm of the B-spline corresponding to the equidistant distribution of knots is studied. Finally, we analyse those types of knot distributions, for which the norms of the corresponding B-splines converge to zero as m .......• 00 .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.